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arXiv · 1309.6037

False Theta Functions and the Verlinde formula

Thomas Creutzig·Antun Milas
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Abstract

We discover new analytic properties of classical partial and false theta functions and their potential applications to representation theory of W-algebras and vertex algebras in general. More precisely, motivated by clues from conformal field theory, first, we are able to determine modular-like transformation properties of regularized partial and false theta functions. Then, after suitable identification of regularized partial/false theta functions with the characters of atypical modules for the singlet vertex algebra W(2,2p-1), we formulate and prove a Verlinde-type formula for the fusion rules of irreducible W(2,2p-1)-modules.

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Thomas Creutzig, Antun Milas. 2014-11-21. False Theta Functions and the Verlinde formula. https://arxiv.org/abs/1309.6037

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